Minerals: Their Constitution and Origin -...

Minerals: Their Constitution and Origin

Minerals: Their Constitution and Origin is an introduc-

tion to mineralogy for undergraduate and graduate

students in the fields of geology, materials science,

and environmental science. It has been designed as

a textbook for use on a semester course and covers

all aspects of mineralogy in a thoroughly modern

and integrated way.

The book is divided into five parts. Part I deals

with the general concepts of structures and bond-

ing within minerals, and introduces symmetry prin-

ciples as well as graphic representations such as

the stereographic projection. It discusses growth, de-

fects, and general issues of isomorphism and poly-

morphism. Part II centers on the physics of miner-

als, including determination of structural features

by X-ray diffraction, an introduction to optical prop-

erties, and the use of the petrographic microscope.

Part III explores the range of naturally forming

minerals and introduces hand specimen identifi-

cation. It gives an overview of the various modes

of mineral formation, and provides a background

in thermodynamics to facilitate an understanding

of mineral equilibria in geological environments

and phase transformations. Part IV provides a sys-

tematic treatment of mineral groups within the

context of mineral-forming environments. Part V

demonstrates the application of mineralogy to the

fields of metal deposits, gems, cement, and hu-

man health. It also explores how minerals form

in the universe, and how they have been active

components at each stage of the evolution of the

earth.

Throughout the text, emphasis is placed on link-

ing minerals to broader geological processes. Unlike

more traditional books on this topic, the authors

also convey the importance of minerals within our

everyday lives and their economic value. Complete

with beautiful color photographs, handy reference

tables and a glossary of terms, this textbook will be

an indispensable guide for the next generation of

mineralogy students.

Hans-Rudolf Wenk is Professor of Geology at the Uni-

versity of California at Berkeley and Andrei Bulakh is

Professor in the Department of Mineralogy at St Pe-

tersburg State University. Both have written many

research papers in the fields of mineralogy, crys-

tallography, geochemistry and tectonophysics, and

have used this extensive expertise to create a com-

prehensive and stimulating textbook.

www.cambridge.org© in this web service Cambridge University Press

Cambridge University Press978-0-521-52958-7 - Minerals: Their Constitution and OriginHans-Rudolf Wenk and Andrei BulakhFrontmatterMore information

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Minerals

Their Constitution and Origin

Hans-Rudolf WenkUniversity of California, Berkeley, USA

and

Andrei BulakhSt Petersburg State University, Russia






www.cambridge.org

C© Hans-Rudolf Wenk & Andrei Bulakh 2004

This publication is in copyright. Subject to statutory exception

and to the provisions of relevant collective licensing agreements,

no reproduction of any part may take place without

the written permission of Cambridge University Press.

First published 2004

Printed in the United Kingdom by Clays, St Ives plc.

A catalog record for this publication is available from the British Library

Library of Congress Cataloging in Publication data

Wenk, Hans-Rudolf, 1941--

Minerals: their constitution and origin / Hans-Rudolf Wenk and Andrei Bulakh.

p. cm.

Includes bibliographical references and index.

ISBN 0 521 82238 6 (hardback) -- ISBN 0 521 52958 1 (paperback)

1. Mineralogy. I. Bulakh, A. G. (Andrei Glebovich) II. Title

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Contents

Preface page xv

Acknowledgments xviii

Figure credits xix

Part I Structural features of minerals 1

1 Subject and history of mineralogy 3

What is mineralogy? 3

History 4

Major directions of investigation 6

Some preliminary advice 8

Definition of crystal and mineral 10

Test your knowledge 10

Further reading 11

2 Elements, bonding, simple structures, and ionic radii 12

Chemical elements 12

Bonding 17

Ionic radii 22

Radius ratio and coordination polyhedra 25

Some general rules concerning ionic structures 30


Further reading 31

3 The concept of a lattice and description of crystal

structures 32

Discovery of the lattice 32

Symmetry considerations 34

The unit cell as the basic building block of a crystal 37

Representation of lattice lines and planes with

rational indices 44

Crystal structure 51


Further reading 53

4 Macroscopic symmetries: crystal morphology 54

Introduction 54

Spherical representations of morphology 54

Point-group symmetry 64

Crystallographic forms 73

Some comments on space-groups 79


Further reading 83






vi CONTENTS

5 Crystal growth and aggregation 84

Nucleation of crystals 84

Habit 85

Twinning 89

Aggregation 92

Multicrystals, porphyroblasts, and poikilocrystals 95

Various growth effects 96


Further reading 101

6 Isomorphism, polymorphism, and crystalline defects 102

Isomorphism and solid solutions 102

Polymorphism and phase transitions 103

Crystalline defects 107


Further reading 113

Part II Physical investigation of minerals 115

7 Experimental studies of crystal structures. X-ray diffraction 117

Basic concepts 117

Brief discussion of waves 119

Laue and Bragg equations 122

The powder method 125

Crystal identification with the powder method 127

X-rays and crystal structure 130

Additional atomic scattering considerations 131


Further reading 133

8 Physical properties 134

Vectors and tensors: general issues 134

Transformation of the coordinate system 136

Symmetry considerations 138

Tensors of different ranks 142

Density 143

Thermal conductivity, thermal expansion, and specific heat 144

Elastic properties 145

Piezoelectricity and pyroelectricity 148

Magnetic properties 150


Further reading 155

9 Optical properties 156

Some physical background 156

Refractive index and the petrographic microscope 157

Polarization and birefringence 164






CONTENTS vii

The optical indicatrix 172

Dispersion 178

Pleochroism 179


Further reading 180

10 Identification of minerals with the petrographic microscope 181

Sample preparation 181

Microscope alignment 182

Determination of the refractive index 183

Use of interference colors 183

Observation of interference figures with convergent light 189

Characteristics of important rock-forming minerals 194


Further reading 207

11 Color 208

Introduction 208

Absorption 208

Fluorescence and phosphorescence 213

Dispersion 213

Luster 213

Microstructure 214


Further reading 216

12 Advanced analytical methods 217

Introduction 217

Diffraction 219

High-resolution imaging 223

Chemical analysis 231

Spectroscopic techniques 233


Further reading 243

13 Mechanical properties and deformation 245

Stress--strain 245

Deformation by slip 245

Dislocation microstructures 248

Mechanical twinning 251


Further reading 252

Part III Variety of minerals and mineral-formingprocesses 253

14 Classification and names of minerals 255

Minerals, mineral species, and mineral varieties 255






viii CONTENTS

Elementary chemical composition 258

Classification of minerals 259

Mineral names 263


Further reading 264

15 Mineral identification of hand specimens 266

Introduction 266

State of aggregation (including crystallographic form

and habit) 266

Color, streak, and luster 267

Mechanical properties 268

Density and specific gravity 271

Other properties 271

Associations of minerals 272

Some directions for practical mineral identification 272


Further reading 275

16 Mineral genesis 276

Mineral genesis and genetic mineralogy 276

Mineral-forming environments 276

Types of mineral crystallization 280

Types of mineral deposit 281

Multistage processes, generations, and parageneses 282

Crystal growth 283

Typomorphism of minerals 284


Further reading 287

17 Stability of minerals. Principles of thermodynamics 288

Introduction 288

Energy minimum in a system 290

The simplest thermodynamic calculations and

diagrams 290

Phase rule 301

Phase diagrams 302

Diagrams for crystallization from a melt 302


Further reading 304

18 Solid solutions 305

Crystallization of solid solutions from a melt 305

Exsolution diagrams 306


Further reading 310






CONTENTS ix

Part IV A systematic look at mineral groups 311

19 Important information about silica minerals and feldspars 313

Introduction 313

Silica minerals 313

Feldspars 318

Brief description of silica minerals and feldspars 326

The origin of granite 330

Pegmatites 335


Further reading 336

20 Simple compounds. Unusual mineral occurrences 337

Introduction 337

Crystal structures and relationships to morphology and

physical properties 337

Brief description of important minerals of the native

elements 342

Unusual conditions of formation 344


Further reading 346

21 Halides. Evaporite deposits 347

Introduction 347

Common compositional and structural features of halides 347

Brief description of halide minerals 349

Origin of halide minerals 351


Further reading 358

22 Carbonates and other minerals with triangular anion

groups. Sedimentary origins 359

Introduction 359

Characteristic features of composition and crystal chemistry

of carbonates and borates 359

Morphology and properties of carbonates. Mineral

associations 363

Brief description of important carbonate minerals 365

Formation conditions of carbonates 367

Carbonates in sedimentary rocks: chemical and biological

origins 368


Further reading 375

23 Phosphates, sulfates, and related minerals. Apatite as a

biogenic mineral 376

Introduction 376






x CONTENTS

Phosphates, arsenates, and vanadates 376

Brief description of important phosphate minerals 376

Sulfates and tungstates 380

Brief description of important sulfate and tungstate

minerals 380

Biogenic processes 384


Further reading 387

24 Sulfides and related minerals. Hydrothermal processes 388

Introduction 388

Crystal chemistry 388

Brief description of important sulfide minerals 392

Sulfide genesis and hydrothermal deposits 396

Weathering and oxidation of sulfides 403


Further reading 405

25 Oxides and hydroxides. Review of ionic crystals 406

Introduction 406

Ionic crystal structures 407

Brief description of important oxide minerals 418

Brief description of important hydroxide minerals 422


Further reading 424

26 Orthosilicates and ring silicates. Metamorphic mineral

assemblages 425

General comments on silicates 425

Orthosilicates 428

Brief description of important orthosilicate minerals 434

Ring silicates 438

Brief description of important ring silicate minerals 438

Metamorphic minerals 440


Further reading 447

27 Sheet silicates. Weathering of silicate rocks 448

Structural features 448

Brief description of important sheet silicate minerals 459

Formation conditions for sheet silicates and weathering

of silicate rocks 462

Clay minerals in soils 463


Further reading 469

28 Chain silicates. Discussion of some igneous and

metamorphic processes 470

Structural and chemical features 470

Brief description of important chain silicate minerals 477






CONTENTS xi

Crystallization of igneous rocks 483

Metamorphic reactions in siliceous limestones 490


Further reading 495

29 Framework silicates. Zeolites and ion exchange properties

of minerals 496

The framework structure 496

Morphology and physical properties 501

Brief description of important framework silicate minerals 503

Ion exchange properties of some minerals 504


Further reading 508

Part V Applied mineralogy 509

30 Metalliferous mineral deposits 511

Introduction 511

Prospecting mineralogy 511

Economically important minerals 512

Geological setting of metal deposits 512

Metal production around the world 523

Reserves 529


Further reading 531

31 Gemstones 532

Introduction 532

Instruments used by gemologists 535

Important gems 538

Gemstone enhancements 542

Crystal synthesis 543


Further reading 549

32 Cement minerals 550

Significance of cement 550

Some features of nonhydraulic cements 551

Portland cement 551

Some problems with concrete 554


Further reading 557

33 Minerals and human health 558

Introduction 558

Mineral-like materials in the human body 558

Minerals in nutrition 560

Minerals as health hazards 562






xii CONTENTS


Further reading 569

34 Mineral composition of the solar system 570

Elements in the universe 570

Minerals of meteorites 572

Minerals of the planets 576

Minerals of the moon 580


Further reading 584

35 Mineral composition of the earth 586

Chemical composition of the earth 586

Composition of the crust 586

Composition of the mantle 588

Composition of the inner core 592

Atmosphere and hydrosphere 593

Mineral evolution over earth’s history 594

Microscopic mineralogy 595


Further reading 598

Appendices 599

1a.1. Metallic or submetallic luster, no cleavage or poor

cleavage, sorted according to hardness 600

1a.2. Metallic or submetallic luster, distinct cleavage, sorted

according to hardness 601

1b.1. Nonmetallic luster, no cleavage or poor cleavage, sorted


1b.2. Nonmetallic luster, single cleavage (platy), sorted


1b.3. Nonmetallic luster, polyhedral cleavage (three systems),

sorted according to hardness 606

1b.4. Nonmetallic luster, prismatic or fibrous cleavage

(two systems), sorted according to hardness 608

2. Minerals that display some distinctive physical properties 610

3. Rock-forming minerals that are colored in thin section 611

4a. Optical isotropic minerals, sorted according to refractive

index 612

4b. Minerals with very low birefringence (up to white

interference colors in 30 �m thin sections), sorted

according to birefringence 613

4c. Minerals with low birefringence (up to first-order red



4d. Minerals with high birefringence (second- to fourth-order








CONTENTS xiii

4e. Minerals with very high birefringence (higher than third-

order interference colors in 30 �m thin sections),

sorted according to birefringence 617

Glossary 618

References 626

Index 635

The plate section is between pp. 290 and 291











Preface

Minerals: Their Constitution and Origin is an intro-

duction to mineralogy for undergraduate stu-

dents and graduate students in all fields of

geology, materials science, and environmental

sciences, and for those with a general interest

in the subject. As a background, the reader is as-

sumed to be familiar with general principles of

physics and chemistry at the high school level.

In this text we introduce principles of crystallo-

graphic and structural features of minerals, as

well as the physical property characteristics used

to identify them. We also provide a survey of the

most important minerals (about 250 and details

for about 100) and their geological occurrence.

The basic types of mineral deposit, both those of

scientific and those of economic importance, are

discussed, often in conjunction with the system-

atic treatment of the mineral classes most closely

associated with particular deposits. The book con-

cludes with a series of chapters on applied min-

eralogy, including a survey of the main industrial

uses of minerals.

There are many excellent mineralogy text-

books, ranging from the early Niggli (1920) mono-

graph (which still contains much of the infor-

mation which is needed), to modern books such

as Putnis (1992), Blackburn and Dennen (1994),

Perkins (1998), Nesse (2000), Hibbard (2002) and

Klein (2002). Why do we add a new book to an

already seemingly saturated market?

To answer this question, we need to look

at how mineralogy courses have evolved. The

modern earth science curriculum, particularly

at American universities, is very different from

that taught 25 years ago. At that time mineral-

ogy was covered with two- to four-semester-long

courses. Today mineralogy has become at best a

one-semester course with two lectures per week

and laboratory sessions. This change in empha-

sis is due to evolving fields such as geomorphol-

ogy, hydrology, climatology, and geophysics that

increasingly have become part of the standard

earth science course load. Yet the importance of

mineralogy for a wide variety of disciplines has

increased. Fields ranging from igneous petrology

to soils science, from archaeology to cement en-

gineering, from materials science to structural

geology make use of mineralogy, and students

from these diverse disciplines need to be accom-

modated. Students do not have time to go into

great detail but they do need to become aware

of basic concepts. Our book provides an alterna-

tive to existing texts by focusing more tightly on

concepts, at the expense of completeness, and by

integrating geological processes and applications

more closely with the discussions of systematic

mineralogy.

Our goal is to be selective in including mate-

rial rather than all inclusive, yet trying to remain

quantitative, scientifically sound, and avoiding

superficiality. It is well known that many stu-

dents are frightened of mathematical expres-

sions. We are using a few equations here and

there, but they can be skipped, without losing

the thread, if students do not have the necessary

background. Since most geology programs re-

quire mathematics and physics courses, it seems

only reasonable to show students that some of

this is useful and can be applied to earth sci-

ences. It brings satisfaction to those who have

taken mathematics courses to see some quantita-

tive relationships, for example how trigonometry

can be used to calculate interfacial angles, basic

thermodynamics to understand a boundary in a

phase diagram, simple linear algebra to appreci-

ate why a second-rank tensor, such as the opti-

cal indicatrix, has the shape of an ellipsoid, or

how complex numbers can be used to add waves

more easily analytically than graphically to ob-

tain diffraction intensities.

One of the biggest challenges in teaching

mineralogy is that some of the most difficult,

theoretically demanding material, is presented

relatively early in the course. There are logical

reasons for focusing on crystal chemistry and

crystallographic topics earlier, rather than later.

Many students have already encountered some

of this background in earlier courses in chem-

istry and physics and there is a natural connec-

tion to these concepts of mineralogy. However, we






xvi PREFACE

do recognize that crystallography is a notoriously

difficult challenge for many students, requiring

them to become adept at three-dimensional visu-

alization, which is often initially difficult. Thus

our treatment of this subject judiciously empha-

sizes the most important concepts so that stu-

dents are not left to wade through pages of ex-

haustive facts that in many cases are better left

for later courses.

The presentation of the text deviates some-

what from the conventional organizational ap-

proach that separates geometry (crystallography),

crystal chemistry, systematic mineralogy, and

petrology. Instead, throughout the book we com-

bine theoretical subjects with experiments, and

discuss larger mineral-forming processes in the

context of specific mineral groups (e.g., the ori-

gin of granite with feldspars). Such an approach

comes naturally and is more likely to focus stu-

dent interest in the subject. The goal has been

to select material that should make it easier to

teach mineralogy and make learning about min-

erals more stimulating.

As mentioned above, our goal is to empha-

size concepts and to minimize nomenclature.

In order not to interrupt the flow of required

material, some case studies and details are in-

cluded in ‘‘technical boxes’’, while ‘‘enrichment

boxes’’ contain supplementary historical mate-

rial or applications. The text includes appendices

covering identification of hand specimens and

optical properties. Some subjects are necessary

background for all aspects of mineralogy: basic

rules of crystal chemistry (Chapter 2), lattice,

and symmetry (Chapters 3 and 4). Many other

chapters are optional and can be skipped at the

discretion of the instructor.

The book is divided into five parts. Part I deals

with general concepts of structures, bonding, in-

troduces the lattice concept, symmetry and crys-

tal forms as well as geometrical representations

such as stereographic projection. It also discusses

growth, defects and general issues of isomor-

phism and polymorphism.

Part II centers on the physics of minerals. First

it shows how to determine by X-ray diffraction

the structural features introduced in Part I. Chap-

ter 8 on physical properties is optional but we in-

clude it because of the importance of this field for

modern geophysics. We introduce optical proper-

ties and the use of the petrographic microscope

early on because most mineralogy courses need

to have this background before mineral systems

are discussed in detail. Clearly parts of Chapter 10

on mineral identification with a microscope rely

on access to relevant laboratory equipment. If

there is no such access to microscopes, or if a

separate course in optical mineralogy is available,

Chapters 9 and 10 can be skipped. Chapter 12,

on advanced analytical techniques, introduces

equipment that may be encountered in modern

mineralogical research laboratories and provides

references for further study.

Part III explores the range of minerals and

introduces hand specimen identification. It also

discusses the wide range of mineral forma-

tion, and provides some background in thermo-

dynamics for understanding mineral equilibria

in geological environments and phase transfor-

mations. Later chapters include applications of

thermodynamics to sedimentary, hydrothermal,

metamorphic, and igneous processes to demon-

strate its relevancy.

Part IV is a systematic treatment of mineral

groups and about 200 of the most important min-

erals. Each chapter combines mineral character-

istics with a discussion of a mineral-forming en-

vironment.

Part V on applied mineralogy deals with top-

ics such as metal deposits, gems, cement, hu-

man health, and explores how minerals form in

the universe and were active components at each

stage of the evolution of the earth. This part is

largely independent of the rest of the book. If

there is no time in class, these chapters can be

used as reading assignments and form good start-

ing points for term projects. The chapters should

illustrate to students that mineralogy is not just

complicated formulas, strange names, Miller in-

dices, and point-groups, but has some practical

significance. This may raise some interest.

Appendices contain determinative tables and

important technical terms are defined in a glos-

sary.

The book is written in a modular fashion that

permits instructors to select or omit some parts,

depending on the level of the course, without

compromising the continuity.






PREFACE xvii

� The content of the whole book seems to us

the minimum one would expect a mineralogy

graduate student to know before entering a

qualifying examination. In that sense it can be

used as a review. Reference is made to more

detailed work to pursue in-depth studies.� A descriptive one-semester course may omit most

of Part II, except perhaps Chapter 11 (Color),

Chapters 17--18 (Thermodynamics, and Solid

Solutions), as well as most of the advanced

boxes. A selection of chapters from Part V can

be useful.� A more analytical one-semester mineralogy course

at major universities would probably touch

only briefly on Chapter 8 (Physical properties),

may omit Chapters 9 and 10 (if no microscope

laboratory session is associated with the

course), Chapter 12 (Additional analytical

methods), and may not have time to include

much of Part V, except for reading

assignments.

The origin of this book goes back to 1993,

when a student from (then) Leningrad visited

Berkeley on an exchange program and brought a

little red book on mineralogy, written by her pro-

fessor, Andrei Bulakh, that caught Rudy Wenk’s

attention because it was exactly the kind of brief

introduction into mineralogy he was looking for.

Over the following years we established further

contact, in part through the exchange of another

student, Anton Chakmouradyan, who came to

play a considerable role in this project. After re-

ciprocal visits to St Petersburg and Berkeley, spon-

sored by the University of California Education

Abroad Program, the authors decided to attempt

to produce an English mineralogy book, in the

spirit of the Russian version, though not a trans-

lation. The different backgrounds of the authors

guarantee a broad view: Andrei Bulakh is a spe-

cialist on alkaline rocks and minerals and geo-

chemistry and has written several books that are

widely used in Russian universities. Rudy Wenk’s

research has emphasized metamorphic rocks, in-

cluding deformation, and investigations of mi-

crostructures in feldspars and carbonates. Both

have taught introductory mineralogy at major

universities for a long time. In this book we have

tried to unite our expertise.

H.-R. Wenk

A. Bulakh






Acknowledgments

This book has benefited from the help of many

colleagues. Some generously contributed illustra-

tions, others reviewed parts of the manuscript

and provided valuable input in discussions. Fore-

most our thanks go to students who, over many

years, taught us what for them is important

in mineralogy, made us appreciate the difficult

subjects, and guided us to topics of most interest.

Mineral photographs were contributed by expert

mineralogists and photographers many of whom

have established a reputation in mineral pho-

tography: Joszef Arnoth from Naturhistorisches

Museum Basel (Arnoth, 1986); Francesco Bedogne

and Remo Maurizio from Sondrio and Vicoso-

prano, respectively (e.g., Bedogne et al., 1995);

Gregory Ivanyuk from Apatiti; Andreas Massanek

from the Technical University of Freiberg (e.g.

Hofmann and Massanek, 1998); Olaf Medenbach

from University of Bochum (e.g., Medenbach

and Wilk, 1986; Medenbach and Medenbach,

2001), Jeffrey Scovil from Phoenix (e.g. Pough,

1996; Scovil, 1996); Erica and Harold Van Pelt

from Los Angeles (e.g., Keller, 1990; Sofianides

and Harlow, 1990); Max Weibel from ETH Zurich

(Weibel, 1973); and a collective of the Museum

of Geology at Beijing (Gao Zhen-xi, 1980). For

other figures we acknowledge Giusseppina

Balassone, Dmitriy Belakovskiy, Dirk Bosbach,

Sherry Cady, John Christensen, Tyrone Daulton,

Peggy Gennaro, Claus Hedegaard, Andreas

Freund, Ray Joesten, Deborah Kelley, Steven

Kesler, Edward Klatt, Maya Kopylova, Sergei

Krivovichev, Michael McQueen, Igor Pekov, Colin

Robinson, Masha Sitnikova, Tim Teague, Mark

Thompson, Roland Wessicken, Tim Wright,

Anatoly Zolotarev and many others as indicated

in the captions. We are appreciative for permis-

sions from publishers to use illustrations from

previous works with details listed under ‘Figure

credits’.

Thorough reviews were provided by Anton

Chakmouradyan (University of Manitoba), Linda

Davis (De Kalb), Keith Dodson (Carmel), Herlinde

Spahr (Orinda), and Julia Wenk (Berkeley) and

greatly improved the text. Comments on indi-

vidual chapters and discussions by Mark Bailey,

Charles Bickel, Douglas Bock, Alain Bulou,

Barbara Hiss, Mike Hochella, Valeriy Ivanikov,

Raymond Jeanloz, George Johnson, Fred Kocks,

Valdimir Krivovichev, David Lawler, Catherine

McCammon, Paulo Monteiro, Andrew Putnis,

Romano Rinaldi, Brandon Schwab, Jim Shigley,

Carlos Tome, Eugeniy Treivus, Paulo Vasconcelos

and Elizabeth Wenk are much appreciated;

and last but not least our copy-editor, Sandi

Irvine. Hart McLeod, Tony Wilkins Illustration,

Cambridge University Press did a wonderful

job in producing this book and its demanding

illustrations. Of course blame for all remaining

deficiencies, omissions and errors in content

rests on the authors and we appreciate the

input from readers who suggest corrections. We

dedicate the book to our wives, Julia Wenk and

Victoria Kondratieva for their patience with us

during this project, which often had to take

preference over family obligations.






Figure credits

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xx FIGURE CREDITS

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Iraq

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S.E. Kesler

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Kluwer Academic Publishers

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Maxwell Museum of Anthropology, University ofNew Mexico

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Figure 12.31: from McKeown and Post (2001).

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NASA

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Oxford University Press

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Royal Geological Society of Cornwall

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Schweizerische Mineralogische und PetrographischeGesellschaft

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FIGURE CREDITS xxi

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xxii FIGURE CREDITS

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